A135750 E.g.f. A(x) satisfies: A(1 - exp(-x)) = 1 + x*A(x).

1, 1, 3, 17, 150, 1869, 30937, 652147, 16971392, 532403448, 19756591654, 854013305595, 42459118750496, 2401987801594055, 153207626004501247, 10930853009024058261, 866325783375527683256, 75806831093269510084028

Offset: 0

Author

Paul D. Hanna, Nov 27 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Programs

Mathematica

Clear[a]; a[0]:= 1; a[n_]:= a[n] =  Sum[k*(-1)^(n - k)*StirlingS1[n, k]*a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 25}] (* G. C. Greubel, Nov 05 2016 *)

Maxima

a(n):=if n=0 then 1 else sum(k*(-1)^(n-k)*stirling1(n,k)*a(k-1),k,1,n); /* Vladimir Kruchinin, Nov 28 2011 */

PARI

{a(n)=local(A=1+x);for(i=0,n,A=1-log(1-x+x*O(x^n))* (subst(A,x,-log(1-x+x*O(x^n)))));n!*polcoeff(A,n)}

Formula

E.g.f. A(x) satisfies: A(x) = 1 - log(1-x)*A(-log(1-x)).

a(n) = Sum_{k=1..n} ( k*(-1)^(n-k)*stirling1(n,k)*a(k-1) ), n>0, a(0)=1. - Vladimir Kruchinin, Nov 28 2011